Developing security and next-generation battery systems have attracted much attention for fulfilled the green development requirements. Among of multivalent-ion batteries candidates, magnesium (Mg) batteries may be the most feasible choice due to its high electrode potential, large theoretical volume capacity, superior safety and abundant source. Nevertheless, the researches of rechargeable Mg batteries still remain at a nascent stage because of a significant challenge of the development of a suitable electrolyte with low flammability and cost, high conductivity, and compatibility with Mg anode. Another major obstacle is lack of an appropriate cathode hosts with large electrochemical window required for Mg2+ insertion. Therefore, recent studies are critical in developing advanced Mg electrolytes with high voltage windows (>4.0 V) and being compatible with Mg-metal anodes to overcome the above-mentioned issues. In this work, we introduce a review on the challenges, development and adopted promising strategies for Mg rechargeable batteries electrolytes. This comprehensive review covers all three classifications Mg-ion batteries electrolytes such as liquid state electrolytes (inorganic electrolytes, boron based electrolytes, magnesium organo-haloaluminate based electrolytes, phenolate or alkoxide salts based electrolytes and non-nucleophilic electrolytes), solid state electrolytes (inorganic solid electrolytes and polymeric electrolytes) and molten salts system (ionic liquid and high temperature molten salts), which can enable researchers to grasp the prevailing challenges, and motivate them to design novel electrolyte candidates for commercial application. (C) 2020 Elsevier B.V. All rights reserved.